Golf is a game of accuracy and repeatability, the objective of the play being to get the ball from a starting point to the bottom of a distant 41/4 inch diameter hole in the fewest number of strokes, and to do so consistently.
While the player is, by far, the largest variable in the process, club design is significant, particularly to the more proficient player, in all of the four basic stages in the ball striking process; i.e., alignment, back stroke, fore stroke and impact.
The distance and direction imparted to the ball are consequent only to the forces and moments produced in the transfer of kinetic energy from the head to the ball in the course of the collision of the two masses. The forces and moments applied by the player through the impact interval are not significant. They are only significant to the process of giving the head mass speed, direction and alignment at the instant prior to impact.
The player, through the shaft, first aligns the striking surface with the target; then, through the shaft, accelerates the head mass in taking it away from the ball, decelerates it to stop it and to change direction, then accelerates it again to bring it back into the ball. In this process of generating the forces and moments to bring about these requisite accelerations, errors by the player are inevitable. The point of impact on the head, the path, position, and attitude of the club head at impact is, therefore, not precisely consistent and predictable.
The forces and moments applied to the shaft inadvertently are reacted by equal and opposite inertial forces and moments of the head mass. The mass and the distribution of the head mass therefore influence the degree of error in the speed, point of impact, path, position, and attitude of the club head at impact, and through impact. Given reasonable mass, length and width, head design is optimized by the prudent distribution of the head mass with relation to the points of application of the stroking and impact forces and moments; i.e., (1) placing as much of the total mass as possible, in essentially equal parts at the extreme ends of the longitudinal dimension; i.e., maximizing both pitch and yaw polar moments of inertia to mass ratio, (k.sup.2)--from the relationship I/m=k.sup.2, where:
I=polar moment of inertia PA1 m=head mass PA1 k=radius of gyration;
(2) placing the point of application of the stroking forces such that there is no yaw moment consequent to the stroking process; and (3) identifying the point of impact producing no yaw or pitch moments at impact.
It is my objective, given reasonable overall dimensions, to maximize k, to insure no yaw moment in the stroke and to minimize the yaw and pitch moments at impact.
Preparatory to striking the ball, the player aligns the club head behind the ball with the intention of moving it away and back into that position with the speed to impact the ball with sufficient energy to cause the ball to travel the desired distance in the desired direction. For the ball to move away from the point of impact on a line to the target, the head mass must be moving on the line with the striking surface square with the line and the ball impacted by that point on the striking surface which produces no yaw or pitch moment; i.e., "the sweet spot"; that point on the striking surface where a force normal to the striking surface passes through the center of percussion. The center of percussion is that point within the physical club head where the mass appears to be concentrated. A square hit on the sweet spot results in maximum energy transfer and a ball departure angle square with the striking surface. The loss of distance and direction, consequent to an error in the point of impact, varies directly with the eccentricity of the hit and inversely with the polar moment of inertia. The rate at which distance and direction are affected by eccentricity of impact, bears directly on consistent play. While such errors are small they are real.
Polar moments about both the yaw and pitch axes are important. While prior designs show some apparent attention to yaw inertia; i.e., "heel and toe weighting," there has been no recognizable awareness of the very substantial significance of pitch inertia.
A "miss" to the right or left of the yaw axis results in both distance and direction errors. A miss above or below the pitch axis, of the conventional club, results in a more significant distance error but without directional error.
The longer the putt, for example, the larger the variation in the actual point of impact. At 25 feet an average golfer will experience a variation of the order of plus or minus 1/2 inch. One putter, typical of putters currently favored by some amateurs and professionals, shows a rapidly changing energy loss with an impact right or left of the center of percussion with a loss at 1/2 inch of some 10% and a directional error of approximately one degree. An impact error above or below the center of percussion results in a more rapidly changing energy loss, with a loss at 1/2 inch of approximately 20%.
I have found that these errors, as well as path and alignment errors, can be substantially reduced by:
optimizing the distribution of the head mass, for maximum polar moments of inertia to mass ratio (k.sup.2) about both the pitch and yaw axes while maintaining sufficient stiffness of the striking surface;
positioning of the point of application of the stroking forces and moments, with respect to the center of mass, center of percussion and neutral axis of the head, to eliminate the inertial moment arm and to stabilize the head in the stroking process; and
the inclusion of a longitudinal member lying on the geometric axis, passing through the center of mass, center of percussion and neutral axis; square with the striking surface and of sufficient length to enhance the alignment process as well as to identify the sweet spot.
In conventional configurations, shown schematically in FIG. 1, the yaw polar moment of inertia of club head 10 is maximized by placing as much of the mass as possible, in equal parts, to the extreme lateral ends, i.e., "heel to toe" weighting of the club head. This results in mass concentrations 12 and 14 interconnected by integral sole and ball-striking flanges 16 and 18, respectively. Concentrating the mass at the heel and toe, however, limits the pitch polar moments and subjects the striking surface to bending.
To achieve the stiffness or resonant frequency required of the striking surface in releasing the energy stored in bending to the ball requires that a significant portion of the club head mass must be placed between the mass concentrations 12 and 14, i.e., in the flanges 16 and 19, thereby limiting the potential polar moment of inertia. In other words, building rigidity into the striking surface in a conventionally designed club by means of a structurally sufficient flange 18 has the undesirable effect of reducing the polar moment of inertia.
If however: (1) the mass is split longitudinally, as in FIGS. 2-10, the connecting member between the mass concentrations is in compression rather than bending. Therefore, the connecting member mass may be reduced to a minimum and moved to the ends of the configuration; thus (2) enabling a higher polar moment of inertia to mass ratio (k.sup.2), with the consequent reduction of stroke and impact errors, but (3) without sacrificing bending stiffness.
(4) Positioning the mass longitudinally substantially increases pitch and yaw polar moments of inertia such that both are maximum and essentially equal.
(5) My arrangement allows for the symmetry required for (a) the positive identification of the center of percussion. Moreover, (b) the longitudinal member facilitates simplification of the alignment process: at address the axis of the longitudinal member is centered behind the ball and on the line through the target. On the backstroke the head is taken away and brought back on the extension of that same axis. The axis and line to the target are coincident in both address and stroke. Finally, (c) the center of percussion, center of mass and intersection of neutral axes are essentially coincident, lying on the longitudinal axis; square with and behind the striking surface. All attribute accuracy in alignment at address and in the course of the stroke.
(6) My arrangement results in the striking surface being well ahead of the point at which the pitch and yaw neutral axes intersect the longitudinal axis. Accordingly, when the point of impact is displaced from the sweet spot, the yaw moment produced at impact is in a direction to reduce the effect of the path and/or attitude errors inadvertent to the fore stroke.
(7) The forward mass accommodates the attachment of the shaft such that (a) the effective point of application of stroking forces lies on the longitudinal axis so that there is no yaw or pitch moment arm on either the back or fore strokes; and (b) the fore and aft location of the stroking force may be positioned forward of the center of gravity for stability in the fore stroke.
These features are optimized in a simple "mallet" configuration (FIG. 2) wherein the fore and aft masses 20, 22 are connected by a thin wall tube 24; the masses 20, 22 being essentially discs or cylinders of high density, high modulus material such as steel, brass, tungsten, and the like.
The rules of golf, however, as set down by the USGA, require that the length (width) of the striking surface be greater than the longitudinal dimension; thus eliminating the simplest, most accurate, most efficient club configuration. The USGA's stated purpose is not to reduce scores, but, rather, to preserve the game of golf. Nevertheless, there are basic configurations of the head mass which can and do comply with USGA rules while achieving the physical properties of the simple mallet arrangement of FIG. 2. For example, the "T" mallet having an extended head as shown in FIG. 3 and the triangle shown in FIG. 4 comply with USGA rules. I do not wish to be understood as eliminating the embodiment of FIG. 2 from the protection of my patent because of the current USGA rules; such rules are subject to change.